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Any two sides of a triangle are together greater than the third side.
Elements of Geometry: Containing the First Six Books of Euclid with a ... - Page 22
by John Playfair - 1855 - 318 pages

The British Annals of Education for ...: Being The Scholastic ..., Volumes 1-2

Education - 1844 - 688 pages
...sides of the one shall be equal to the angle contained by the two sides equal to them of the other. 3. Any two sides of a triangle are together greater than the third side. 4. The straight lines which join the extremities of two equal and parallel straight lines towards the...

Proceedings, Volume 10

Royal Society of Edinburgh - Science - 1880 - 866 pages
...: — That the greater side of every triangle has the greater angl* opposite, and conversely. That any two sides of a triangle are together greater than the third side. Also Euclid I. 21. Euclid I. 24 and 25. Euclid I. 26 (the second part). Also the usual propositions...

A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 434 pages
...together less than AB, the circles would not intersect, and the construction, would be impossible ; hence any two sides of a triangle are together greater than the third, which is established in a different manner in (Prop. 13.) PROPOSITION V. — THEOREM. If two triangles,...

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...pass through the point A, let it fall otherwise, if possible, as FGDH, and join AF, AG. Then, because two sides of a triangle are together greater than the third side, (i. 20.) therefore FG, GA are greater than FA : but FA is equal to FH ; (i. def. 15.) therefore FG,...

The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...not equal to AB : therefore AC is greater than AB. Wherefore, if two angles, &c. PROP. XX. THEOB. — Any two sides of a triangle are together greater than the third side.t * Let the learner compare thia proposition and the following with the 5th and G1h of this book....

The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 130 pages
...It has been shown that AC ^ AB, AC > AB. Therefore the greater Z., &c. PROP. XIX. THEOR. 20. 1 Eu. Any two sides of a triangle are together greater than the third side. Let ABC be a <^, then AB + AC> BC, AB+ BOAC, BC + AC> AB. Produce BA to D. Make AD = AC. Prop. s. Join DC. Then...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...the triangle, but contain an angle BDC greater than the angle BAC. Produce BD to E : Then, because any two sides of a triangle are together greater than the third side (1. 20), the two sides, BA, AE, of the triangle ABE are greater than BE : To each of these add EC ;...

Practical Geodesy: Comprising Chain Surveying, and the Use of Surveying ...

Sir J. Butler Williams - Geodesy - 1846 - 368 pages
...the true length : this follows from Euclid's 20th proposition of the first book, which proves that any two sides of a triangle are together greater than the third. Also, the frequent repetition of errors in the coincidence of the extremities of the chain with the...